Variance Estimation in Nonparametric Regression via the Difference Sequence Method
نویسندگان
چکیده
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for suitable asymptotic formulations our estimators achieve the minimax rate.
منابع مشابه
Variance estimation in nonparametric regression via the difference sequence method (short title: Sequence-based variance estimation)
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for ...
متن کاملVariance Estimation in Nonparametric Regression via the Difference Sequence Method by Lawrence
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for ...
متن کاملVariance estimation in nonparametric regression via the difference sequence method ( short title :
Consider the standard Gaussian nonparametric regression problem. The observations are (xi, yi) where and where ~i are iid with finite fourth moment p4 < oo. This article presents a class of difference-based kernel estimators for the variance *AMS 2000 Subject Classification 62G08, 62G20 t ~ e ~ w o r d s and Phrases: Nonparametric regression, Variance estimation, Asymptotic minimaxity he work o...
متن کاملDerivative estimation based on difference sequence via locally weighted least squares regression
A new method is proposed for estimating derivatives of a nonparametric regression function. By applying Taylor expansion technique to a derived symmetric difference sequence, we obtain a sequence of approximate linear regression representation in which the derivative is just the intercept term. Using locally weighted least squares, we estimate the derivative in the linear regression model. The ...
متن کاملOptimal Difference-based Variance Estimation in Heteroscedastic Nonparametric Regression
Estimating the residual variance is an important question in nonparametric regression. Among the existing estimators, the optimal difference-based variance estimation proposed in Hall, Kay, and Titterington (1990) is widely used in practice. Their method is restricted to the situation when the errors are independent and identically distributed. In this paper, we propose the optimal difference-b...
متن کامل